Dr. David L. Nersessian has written an article on “How State Legislative Bans on Foreign and
International Law Obstruct the Practice and Regulation of American Lawyers.” It will be published in the Arizona State Law Journal, but you can read the paper now by clicking here. It's a good piece of scholarship and will likely be an often-referenced source of information on the initiatives that states have promulgated to try to prohibit the citation of foreign or international law in state judicial decisions. Here's the abstract of his article:

Thirty-three state legislatures have introduced (and five have enacted)
“blocking” initiatives that prohibit foreign or international law in state
judicial decisions. Some states, such as
Oklahoma, extend this ban to religious tenets, notably Sharia law. Scholarly discourse to date has focused
principally upon how such legislation discriminates against minority religious
groups. The academic community has yet
to consider the serious collateral (and apparently unintended) impact of such
laws on the American legal profession itself, which is the subject of this
article.

Blocking laws make it all but impossible for practicing lawyers to
fulfill their ethical obligations in legal matters abroad, which forces them
either to decline legal work overseas or to risk violating foreign laws. Blocking initiatives also create uncertainty
about ethical duties at home whenever domestic legal work includes a transnational
dimension. Such laws resurrect the
“double deontology” problem (where inconsistent ethical duties apply
simultaneously) that the revised ABA Model Rules intended to solve. They also eviscerate the Rules’ safe harbor
protection on difficult choice of law questions.

Blocking measures also interfere with wider regulatory structures. They infringe unconstitutionally on the power
of state judiciaries to prescribe substantive ethical rules and to regulate
lawyer conduct abroad. They also disrupt
reciprocal discipline between American states and relationships between state
judiciaries and federal courts. But this
confluence of negative outcomes is completely unnecessary because judges have
sufficient tools already to guard against potential abuses in the application
of foreign or international law.

Apart from invalidating existing laws as unconstitutional, there should
be a concerted effort by American lawyers, state judiciaries, and bar
organizations to oppose such initiatives becoming law in the first place. There certainly is room for spirited
disagreement over the proper role of foreign and international law in American
courts. But this requires a genuine
debate, not legislative ultimatums that foreclose all further
consideration. Blocking laws essentially
require American lawyers (not to mention judges – members of co-equal branches
of state government) to pretend that foreign and international law do not
exist. Such proposals are neither
workable nor wise, and they amount to little more than misguided hope that
certain global legal realities – if sufficiently ignored – might simply go
away.